New geometric shape 'Gomboc' featured at Expo
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Erno Rubik's magic cube may be Hungary's most well-known contribution to the world's stock of inventions, but at the 2010 Shanghai Expo, the Hungarians are promoting another eye-catching mathematical product -- "Gomboc."
Gomboc, a curious new solid shape which can gradually rock itself back to equilibrium when disturbed, was invented in 2006 by two Hungarian engineers.
In May, it made its public debut when it became the centerpiece of the Hungarian pavilion at the World Expo in China.
With a roughly two-meter tall lumpy stainless steel shape, Gomboc serenely rests in the center of the 1,000-square-meter space, challenging visitors to work out what exactly it is. A work of art, science or perhaps mathematics? No one seems entirely sure.
Despite the deliberate lack of explanation accompanying the display, the odd-shaped object has been one of the hits of the Expo, as the Hungarian pavilion is among the ten biggest attractions of the event.
In a recent exclusive interview with Xinhua, Hungarian scientists Gabor Domokos and Peter Varkonyi, who proved the existence of Gomboc in 2006, described the new object as a "meeting place for mathematics, harmony, balance and beauty."
Inventing a new shape takes time. The search for what would become this strange new form goes back 20 years when Domokos, Professor of Mechanics, Materials and Structures at the Budapest University of Technology and Economics, began toying with the idea of a shape or solid which balances in a stable manner at only one point.
Along with American colleagues Andy Ruina and Jim Papadopoulos, he proved that such a shape does not exist and took the conclusion to a mathematics conference in Hamburg in 1995, where the famed Russian scientist and mathematician Vladimir Arnold was speaking.
Arnold died in June 2010 at the age of 72, but as Domokos recounted, Arnold played a leading role in the story of Gomboc.
During the conference, Arnold listened to Domokos's results, and told him he was looking for the new shape in the wrong place.
According to Domokos, Arnold posed a question to him: "Is it possible to build a three-dimensional homogenous solid which has no more than two equilibrium points, one stable point and one unstable one, like the tip of a pencil?"
"Science is about questions, not answers, so questions are like hard currency," Domokos said.
"This was a gift from Arnold. It is such a fundamental question that it could have been asked by Archimedes. For thousands of years no one looked for this solid, and now I had my mission. All the glory now surrounding this Gomboc came from Arnold's question," Domokos said.
Domokos returned to Budapest energized, and set out to realize Arnold's hypothetical shape.
Around 2004, Varkonyi, a 25-year-old graduate student of Domokos at the time, joined the search. They worked together, getting closer to a proof. Almost 12 years after Domokos's encounter with Arnold in Hamburg, the theoretical existence of the new shape conclusively emerged in 2006.
"The initial proof of existence turned out to be much longer and more complicated than we expected. I think it was partly because we are engineers rather than mathematicians, and not very experienced in differential geometry, but we never thought of giving up," Varkonyi recalled.
Their engineering background pushed them to go further with the new-born shape. "We wanted to make it real, to build it, to be able to touch it," Domokos said.
In 2007, a prototype was produced after many failed experiments. "If the first one had not worked, we would have given up, because of the costs," Domokos said.
License fees and expensive technological experiments were draining the cash reserves. By this time though, a buzz about the new shape had begun. The story of the breakthrough proof appeared on the front page of the prestigious journal The Mathematical Intelligencer. The New York Times ran a feature on the "self-righting object." Then the Hungarian government said it wanted Gomboc to represent the country at the Shanghai Expo and agreed to finance its licensing and legal costs. The future was secure.
"When we chose it, we had no idea it would become famous," Domokos said.
Although Gomboc has the unique property of being the only solid with two equilibria, one stable, one unstable, its actual shape has infinite, although mostly sphere-like, varieties.
Thanks to the Shanghai Expo, Gomboc has become popular in China. 0 "Chinese people think about Gomboc more easily than Europeans," Domokos said. "The visitors to the pavilion don't seem to need so much technical information, they are happy with just the shape. Many people go home trying to figure out what they have just seen and come back the next day for another look."
"Generally, I find Chinese people more sensitive to shapes, to motion and harmony. They look at things as a whole. In the West, we try to understand the differential geometry of Gomboc. The Eastern approach, however, is more philosophical. According to some in China, Gomboc is an analogy of yin and yang, and some say it goes even further back to the 6,000 year-old roots of Chinese philosophy," Domokos said.
"So if we can get Oriental people thinking like that about something which originates from here, then it is useful. From those ideas we will get back something in the West which we don't know," Domokos added.
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